This is the 2817th most frequent Polish word.
kartkę
"Kartkę" means "a piece of paper" in English.
In this sentence, 'kartkę' refers to a sheet or piece of paper, used in its accusative singular form as the direct object.
Mam kartkę papieru.
I have a piece of paper.
Here, 'kartce' is in the locative singular form, indicating the location where the action took place.
Napisałem coś na kartce.
I wrote something on the piece of paper.
In this context, 'kartkę' is used in the accusative singular form to signify what is being requested.